A292982 - OEIS

%I #11 Dec 13 2017 02:47:16

%S 24,30,40,42,48,54,56,66,70,72,78,80,88,96,102,104,114,120,138,150,

%T 160,162,168,174,186,192,210,216,222,224,240,246,258,264,270,280,282,

%U 288,294,312,318,320,330,336,352,354,360,366,378,384,390,402,408,416,420

%N Bi-unitary abundant numbers: numbers n such that bsigma(n) > 2n, where bsigma is the sum of the bi-unitary divisors function (A188999).

%C Analogous to abundant numbers (A005101) with bi-unitary sigma (A188999) instead of sigma (A000203).

%H G. C. Greubel, <a href="/A292982/b292982.txt">Table of n, a(n) for n = 1..10000</a>

%e 24 is in the sequence since bsigma(24) = 60 > 2*24.

%t f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bsigma[m_] :=

%t DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; bAbundantQ[n_] := bsigma[n] > 2 n; Select[Range[1000], bAbundantQ] (* after _Michael De Vlieger_ at A188999 *)

%o (PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }

%o gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));

%o biudivs(n) = select(x->(gcud(x, n/x)==1), divisors(n));

%o isok(n) = vecsum(biudivs(n)) > 2*n; \\ _Michel Marcus_, Dec 13 2017

%Y Cf. A005101, A034683, A188999.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 27 2017